30Spline - Nonparametricregressionusingsmoothingsplines

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Unformatted text preview: Nonparametricregressionusingsmoothingsplines Smoothingisfittingasmoothcurvetodatainascatterplot Willfocusontwovariables: Y andone X Ourmodel: y i = f ( x i )+ i , where 1 , 1 ,... n areindependentwithmean0 f issomeunknownsmoothfunction Uptonow f hasaspecifiedformwithunknownparameters f couldbelinearornonlinearintheparameters, functionalformalwaysspecified If f notdeterminedbythesubjectmatter,wemayprefertoletthe datasuggestafunctionform c 2011Dept.Statistics(IowaStateUniversity) Stat511section30 1/50 Whyestimate f ? canseefeaturesoftherelationshipbetween X and Y thatare obscuredbyerrorvariation summarizestherelationshipbetween X and Y provideadiagnosticforapresumedparametricform Example:DiabetesdatasetinHastieandTibshiranisbook GeneralizedAdditiveModels Examinerelationshipbetweenageofdiagnosisofdiabetesand logoftheserumC-peptideconcentration Hereswhathappensifwefitincreasingordersofpolynomial,then fitanestimated f c 2011Dept.Statistics(IowaStateUniversity) Stat511section30 2/50 5 1 1 5 3 .0 4 .0 5 .0 6 .0 Age at Diagnosis lo g C- p e p t id e c o n c e n t r a t io n c 2011Dept.Statistics(IowaStateUniversity) Stat511section30 3/50 5 1 1 5 3 .0 4 .0 5 .0 6 .0 Age at Diagnosis lo g C- p e p t id e c o n c e n t r a t io n linear fit c 2011Dept.Statistics(IowaStateUniversity) Stat511section30 4/50...
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This note was uploaded on 02/11/2012 for the course STAT 511 taught by Professor Staff during the Spring '08 term at Iowa State.

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30Spline - Nonparametricregressionusingsmoothingsplines

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